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首页> 外文期刊>Plasma physics and controlled fusion >'Quasi-local' wave equations in toroidal geometry with applications to fast wave propagation and absorption at high harmonics of the ion cyclotron frequency
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'Quasi-local' wave equations in toroidal geometry with applications to fast wave propagation and absorption at high harmonics of the ion cyclotron frequency

机译：环形几何中的“准局部”波动方程及其在离子回旋加速器频率高谐波下快速传播和吸收的应用

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摘要

The integral constitutive relation for high frequency waves propagating in toroidal axisymmetric plasmas, obtained by formal integration of the linearized Vlasov equation, is simplified assuming the range of spatial dispersion to be small compared to the linear dimensions of the plasma. We propose to call this the 'quasi-local approximation'. A (formally infinite) system of purely differential wave equations is obtained, which should be a good approximation under conditions similar to those which would justify an Eikonal Ansatz for the form of the wave fields. This system is valid to all orders in the Larmor radius, and, in the presence of a poloidal static magnetic field, predicts a different plasma response to each poloidal Fourier component of the h.f. field. Compared to ray tracing based on the Eikonal approximation, these. wave equations have the advantage of allowing to take into account periodicity, boundary conditions, and toroidicity-induced coupling between poloidal Fourier modes. As an example, the quasi-local wave equations are used to model. propagation and absorption of the compressional wave at frequencies higher than the ion cyclotron frequency in the high-P plasma of the National Spherical Tokamak Experiment in Princeton, USA. Because of the low magnetic field and the tight aspect ratio of this device, large Larmor radius effects and toroidicity play an important role in these experiments. This example, therefore, illustrates well the importance of taking into account these effects, and, in particular, the different response of the plasma to each poloidal Fourier mode. [References: 21]
机译：通过线性化Vlasov方程的形式积分获得的，在环形轴对称等离子体中传播的高频波的积分本构关系得到简化，并假设与等离子体的线性尺寸相比，空间色散的范围较小。我们建议将其称为“准局部逼近”。得到了一个（微分形式的）纯微分波动方程组，在与证明Eikonal Ansatz证明其波场形式合理的条件类似的条件下，它应该是一个很好的近似值。该系统对拉莫尔半径上的所有阶数均有效，并且在存在倍数静磁场的情况下，可以预测对h.f.的每个倍数傅里叶分量的不同等离子体响应。领域。与基于Eikonal近似的光线跟踪相比，这些。波动方程的优点是可以考虑到周期性，边界条件以及由极向性傅立叶模态之间的圆环性耦合。例如，使用准局部波动方程进行建模。在美国普林斯顿国家球形托卡马克实验的高P等离子体中，压缩波在高于离子回旋加速器频率的频率下的传播和吸收。由于该设备的磁场低且纵横比很窄，因此较大的拉莫尔半径效应和环形性在这些实验中起着重要作用。因此，该实施例很好地说明了考虑这些影响的重要性，尤其是考虑到血浆对每种多倍傅立叶模式的不同响应。 [参考：21]

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